Selective-constant-resistance network



2 Sheets-Sheet l O. J. ZOBEL sELEcTIvE CONSTANT RESISTANCE NETWORK Filed April 13. 1928 mfg. 20, 1929.

INVENToR BY 0. JZoe ATTORNEY Aug. 20, 1929. o. J. zoBEL SELECTIVE CONSTANT RESISTANCE NETWORK 2 Sheets-Sheet 2 Filed April 13, 1928 IllL lNvENoR 0. J Zoe ATrRNEY Patented Aug. 20, 1929.

UNITED STATESv PATENT oFFlcE- OTTO J. ZOBELJ OF NEW `YORK-,'N. Y., ASSIGNOR TO AMERICAN TELEPHONE AND TELE- GRAPH 4COIMIIPANY, A CORPORATION OF NEW YORK.

' SELF.CTIVE-CONSTANT-RESISTANCE NETWORK.

Application filed April 13*I The principal object of my invention is to provide apparatus for convenient and effective use to filter components according to frequency from a sequence of composite electric waves. Another object of my invention is to provide apparatus for performing this operation with advantageous impedance values at all frequencies. Another object is to provide an electric wave lter or selective network having substantially constant input impedance at practically all Jfrequencies. These objects, and various other objects of my invention, will become apparent on consideration'of alimited number of specific examples 15 of practice according to the invention, which I have chosen for presentation in the following specification. It will be understood that this disclosure relates principally to these particular exainfples of the invention, and

that the scope o the invention will be indicated in the appended claims.

Referring to the drawings7 Figure 1 is a diagram of a ladder type filter, with generalized elements indicated symbolically and showing various terminations at the input end; Fig. 2 is'adiagram of a mid-series section to be substituted in the filter of Fig. 1. Fig. 3 is a diagram of a mid-shunt section to be substituted in the filter of Fig. l; Fig.' 4

is a diagram of a lattice typefilter, of general form; Fig. 5 is a diagram of a section for a more special lattice type lter; Fig. 6

is a diagram of an elementary filter; F 7

is a diagram of a mid-series low pass filter section with infinite networks for certain elements; Fig. 8 is a corresponding diagram with finite terminations for the networks;

Fig. 9 is a diagram of a mid-shunt low pass lilter section with finite endings for thenetworks comprised therein; and Fig. 10 is an assembly of diagrams for attenuation and phase shift in various filters considered herein. Y

In Fig. 1, a ladder type filter is shown, with recurrent alternately disposed series impedances .el and shunt impedances z2. This network has a pairof input terminals at the left. The theory of such networks is ordinarily de'- veloped on the initial assumption that the recurrent structure extends to infinity from the input terminals; this is indicated by the 1928. Serial No. 269,845.

dotted lines at the right.' Of course, 'any series impedance a,

2 al. Also, any can be replaced with equivaparts in series, each of value shunt element z2 may be separated into two equal lent effect by two shunt elements in parallel,

each oimpedance value 222. it will be readily apparent that if the input terminals are taken at aa, the ending may be called full series; if at bb, it is mid-series; ifV at ce, it is full shunt; and if at ald, it is mid-shunt.

The corresponding input impedances are:

Kn 1/ 'l' Z1/2 K.. am (2)' Km: #51m-J2 (3) K... 2.a/ #ma 4) The foregoing results may be readily established by reference to pages 34 and 35 of my paper on Theory and design of uniform and composite electric wave filters in the Bell System Technical Journal for January, 1923.'

A section of the ladder type ilter as from ZZ to mm is called a mid-shunt section; from pp to w' is a mid-series section'.

The propagation constant 1 for the ilter of Fig. 1 is given by the following formula er= 1 @222+- 2l/a+ maar r 5) This formula may be deduced from formula `7 of page 34 of the paper above mentioned.

After starting the development of the theory of the ladder type electric Wave filter,

as above, with an infinite number of sections, it is usual to show that the practical operation is almost the same with a moderate finite number of sections and a suitable terminal net-- work N; this may be connected in Fig. l by where =R is a constant real number. The

I l(e) that I f 1, is representedb dition -By substituting in Equation (5) from a Equation (6), the formula for the propagatiol constant of the constant R filter is shown to e ef=1+z,/2R2+z/(4R2+a2)/R2' (8)' In the eneral network lof Fig. 1, with midseries en ing at bb, let each mid-series sectionl such as from pp to 'rr be as shown in Fig. 2, where` each half series impedance,

521, is represented bythe infinite network 'between and extending up from the points gg, and where each shuntelement, z2 of Fig.

2z Let the zs of ig. 221'be,subject to the con- "1iz=R24 (9) The impedance of eachv lnetwork representing that is, the impedance across the oints gg, may be obtained by the aid of quation (3), then, withfthe result so obtained, the mid-series characteristic impedance of Fig. 1, with its elements replacedl as in Fig. 2, may be worked out. In this case,

the result will be R. s

That is, if`the general impedances ,of the filter. of Fig. 1 are replaced according to the more special values shown in Fi .12, subject to Equation (9), then the dou l'y'infinite 1' structure obtained in this way, with mid-series input termination', has a constant input im edance R. at all frequencies. I v

gain, suppose that the general filter of Fi .fl'isA given the more special form in which eac midhunt section as from ZZ to is replaced by the-structure of Fig. 3. By a procedure similar to' that for Fig. 2,4 it can be shown that the filter obtained according to Fig. 3 will have the mid-shunt 'characteristic imladances of constant value R.

bo'th eases, thatis, for Fi tion constant will be igio'vei by the ollowmg formulal derived m Equation 5),

Instead of the ladder type filters con-l mid-series ending, Fi 3 ,amid-shunt ending;'

1 made dea'.

p nite according to Fig. 2 or Fig. v3, the Propa- .are Very ance is given by i l K1: VZlZg 4 and the propagation, constant by f Z122'- Z1 Equations (11) and (12) follow from Equation (23) on page 19 of my paper mentioned above. In the iilter shown in Fig. 4, let the generally expressed impedances, and 2.22, be replaced by the corresponding infinite networks shown 1n Fig. 5. In other words, Fig. 5 representsa single section of the filter of Fig. 4,

with the general impedances of Fig.- 4 made more' specic as shown in Fig. 5. Let the zs of Fig. 5 be subject to the condition The coefiicient appearing in the expressed values of the terminal impedance elements of Fig. 5 may have any convenient value from zero to 1. The impedance across the points hh in Fig. 5 can be obtained by the aid of Equation (3), and likewise across the points hh.' The impedance across the points jj can be found by the aid of Equation (1), and likewise across the points jy". With these impedance values so obtained, the impedance of the ininite network of Fig. 4, with sections as in Fig. 5, may be obtained -b the aid of Equation (11), and, subject to tlie condition expressed in Equation 13), it works out to.

structions for wave ilters'of constant resist-R:

both these are of la der type, and Fig. 5 is of'lattice type. .These Figs. 2, 3 and 5 are specific when compared with the more general Figs. 1 and 4, but, on the other hand,'they gleneral for the class of constant resistance 4c aracteristic impedance filters; soA eneral that they-may represent low pass or 'gh pass, or band pass, or low-and-high pass filters. i

In'iny paper inthe Bell System Technical Journal, referred to above, I have -shown on ance characteristic impedance; Fig. 2 has a page 6 and context how to design the series and shunt impedances (respectively all, and 221.-) of a constant c wave filter, so that it will have any pre-assigned transmitting and attenuating bands, subject to the condition that the product of the said series and shunt impedances shall be k2. The principles of this paper may be applied to the filters of Figs. 2, 3 and 5, and those figures can be made more specific than they are shown, to get any desired attenuating and transmitting ranges; this I will now demonstrate.

Consider the ladder type filter of Fig. G, whose series impedances are each zu of Figs. 2 and 3 and whose shunt impedances are each z2, of those figures. Fig. 6 represents a constant lo wave filter, according to Equations (6) and (9), where, in the notation of my paper just referred to, 211:21?, and @21:22h. Its propagation constant F,.- is given by replacing z, by zu and 22 by z2, in Equation (5). But the same value vill be obtained by squaring Equation (10). Hence This shows that at each frequency the propagation constant of the filter of Figs. 2 or 3 is half that of Fig. 6. In other words, two sections of Fig. 2 or Fig. 3 have just the same propagation constant as one section of Fig. 6. Now by the principles of my paper above referred to I can assign values to zu and z2, of Fig. 6 to get any desired transmitting and attenuating bands; and thc values of zu and am, so determined, are to be introduced in Fig. 2 Vor Fig. 3.

As to the filter of Fig. 5, if :1::0, it can be shown that two sections of this lattice type filter become equivalent to a single section of the ladder type filter of. Fig. G. Hence, the procedure to design Fig. 5 for a special purpose is to begin with Fig. (i, as outlined above for the ladder type.

ISpecifically to illustrate thev further procedure, let us assume that the desired filter is to he a low pass filter cutting off at a definite given frequency f2. Such a filter' may be of ladder type as in Fig. 6, with series inductances 12,7. and shunt capacities 021.-, so that 2.=ft-27'L and A (16) 221: Yi/QvrOgi- By Equation (6), A x

RgzLl-f/Oa By page 39 of my paper heretofore mentioned, the critical or cut-off frequency of this filter is given by Hence the design equations for this filter are stant.

and accordingly the filteriof Fig. r2 takes the form shown'in Fig. 7 with We have now progressed to the point for passing from the infinitely upward extending networks to the finite' networks with proper terminations; these are shown in Fig. 8. The design and the values for the terminal elements are determined according tothe principles set forth in my paper hertofore mentioned. Extending upwardly from the points gg, in succession, are

One and one fourth mid-shunt sections,

One mid-half section, M-typc, where m=3/5.

Resistance termination R. These are embodied as follows: L1, O2 and 03 have the values stated heretofore;

5 15 l0 L5 ELI; 8 L17 The recurrent network extending upwardly from the points gg is in itself a high pass filter, and it is terminated in such manner that Within its pass range its input impedance is a pure resistance and lapproximately constant.

Again, dealing with Fig. 3 instead of Fig. 2, the desired low pass filter may be shown to take the form presented in Fig. 9, in which L, and U3 have the values stated heretofore, and

If the desired low pass filter is to be of lattice type as in Fig. 5, then in each section one pair of non-adjacent impedances will be the same vas looking upwardly across the points gg in Fig. 8; and the other such pair will be the same as looking into the shuntnetwork across the points tt in Fig. 9. The factor a" of Fig. 5 is taken at zero value.

Let I be separated into its real and imaginary parts, thus 1"=A +713, where 'A' is the attenuation constant and B is the phase 'con- I have computed A and B over a wide range of frequencies for each of the single filter sections of Figs. 7, 8, 9 and 5 with the special elements for Fig 5 mentioned above. The results are plot-ted in Fig. 10. The curves for the two ladder type filters of F igs. 8 and 9 are so close together as to be almost indistinguishable and I have not attempted practical filter, and only in art-due to the,

finite endings for the impe ance networks within each filter section as compared with the infinite extent of those networks shown in Fig. 7. The curves of Fig. 10 are in each case for .a single filter section; for any number of sections the ordinates should be multiplied by that number, butl obviously the percentage departures of the practical filters from'the ideal filter will remain the same.

The impedance of these three practical networks have also been worked out on the same basis and compared with the impedance R for the corresponding ideal networks. For all three networks and at all frequencies from zero to 2;"2 the modulus of the impedance is within 2% of the value R and the angle of the impedance within 2. For most frequencies the departures are much less than 2% and 2.

The attenuation constants, phase constants and impedances for the three practical filters mentioned were all Worked o uton the basis of an infinite number of sections, each section like Fig. -8 or 9- or 5 (with special elements) respectively. On this basis the characteristic impedance `is found to be nearly of constant value R. Therefore, a small inte- Ural number of sections may bey chosen and iheterminal network N of Fig. 1 may lbe employed, this being simply a resistance R. For such afinite filter the in ut impedance will be very nearly R and t e attenuation and phase constant will be very nearlyas shown A lter made according to my invention may be connected toreceive input from a line or, other. transducer of resistance R, and the filter .output maybe connected to receiving apparatus of resistance R. Several filter sections with the same characteristic impedance R but different attenuation values A'and dif ferent phase shifts B may be connected di- 1. Al selective constant resistance network ofthe' type having like recurrent sections,

with'. means forming! a part of each section to make'the characteristic impedance substantially a` constant ure resistance for a wide '..Ian'ge-of'frequenc1es both within and Without the range ofthe network.

.mentioned network to give it approximately la constant resistance in .its .transmitting range, the characteristic lmpedance lof. the

2. A selective constant resistance network of the type having like recurrent sections, an element of substantially constant pure re sistance connected with the network output terminals, and means in each section to make the characteristic impedance the same as said resistance for a wide range of frequencies both within and without the pass range of the network.

3.,An electric Wave filter, a selective constant resistance network consisting of a network of like recurrent sections, cach section comprising a plurality of impedances, atleast one in series and at least one in shunt,- atleast one. of these impcdances ineach section being another network of like recurrent sections, the characteristic impedance of the filter being substantially a constant res istance for a wide range of frequencies both within and Without the pass range of the filter. l 4. An electric wave filter, a selective ccnstant resistance network consisting of a network'of like recurrent sections, each section comprising a plurality of impedances, at least one in series and at least one in shunt, atleast one of these impedances in cach section being another network of like recurrent sections, and a terminal network for each such'last filterbeinga constant resistance for a wide range of frequencies bothwithinand without the pass range of the filter. 5; A selective constant resistancc'network of sectional ladder type, each section having at least one series impedance and at least one shuntimpedance and each section also having a network with series and shunt elements .associated with one of said impedances to 'make thel characteristic impedance lof the.

mainnetwork substantially a constant pure resistance for a wide range of frequencies both within and without the network.

6. An electric wave filter, stant resistance network of sectional ladderl type with mid-series or mid-shunt ending at, both ends, an element of substantially constant pure resistance connected with the filter the pass frange of a-selective coni A output terminals, and means in each section to' give the filter an input impedance at substantially all frequencies equal to 'said constant resistance.

In testimony whereof, I havesignedmy name to this specification this 12th day of April 1923.

i j L OTTO-J. zoBEL. 

